5,095 research outputs found
Differentiability of quadratic BSDEs generated by continuous martingales
In this paper we consider a class of BSDEs with drivers of quadratic growth,
on a stochastic basis generated by continuous local martingales. We first
derive the Markov property of a forward--backward system (FBSDE) if the
generating martingale is a strong Markov process. Then we establish the
differentiability of a FBSDE with respect to the initial value of its forward
component. This enables us to obtain the main result of this article, namely a
representation formula for the control component of its solution. The latter is
relevant in the context of securitization of random liabilities arising from
exogenous risk, which are optimally hedged by investment in a given financial
market with respect to exponential preferences. In a purely stochastic
formulation, the control process of the backward component of the FBSDE steers
the system into the random liability and describes its optimal derivative hedge
by investment in the capital market, the dynamics of which is given by the
forward component.Comment: Published in at http://dx.doi.org/10.1214/11-AAP769 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Effects of short-range interactions on transport through quantum point contacts: A numerical approach
We study electronic transport through a quantum point contact, where the
interaction between the electrons is approximated by a contact potential. Our
numerical approach is based on the non-equilibrium Green function technique
which is evaluated at Hartree-Fock level. We show that this approach allows us
to reproduce relevant features of the so-called "0.7 anomaly" observed in the
conductance at low temperatures, including the characteristic features in
recent shot noise measurements. This is consistent with a spin-splitting
interpretation of the process, and indicates that the "0.7 anomaly" should also
be observable in transport experiments with ultracold fermionic atoms.Comment: 12 pages, 10 figure
Low-rank Linear Fluid-structure Interaction Discretizations
Fluid-structure interaction models involve parameters that describe the solid
and the fluid behavior. In simulations, there often is a need to vary these
parameters to examine the behavior of a fluid-structure interaction model for
different solids and different fluids. For instance, a shipping company wants
to know how the material, a ship's hull is made of, interacts with fluids at
different Reynolds and Strouhal numbers before the building process takes
place. Also, the behavior of such models for solids with different properties
is considered before the prototype phase. A parameter-dependent linear
fluid-structure interaction discretization provides approximations for a bundle
of different parameters at one step. Such a discretization with respect to
different material parameters leads to a big block-diagonal system matrix that
is equivalent to a matrix equation as discussed in [KressnerTobler 2011]. The
unknown is then a matrix which can be approximated using a low-rank approach
that represents the iterate by a tensor. This paper discusses a low-rank GMRES
variant and a truncated variant of the Chebyshev iteration. Bounds for the
error resulting from the truncation operations are derived. Numerical
experiments show that such truncated methods applied to parameter-dependent
discretizations provide approximations with relative residual norms smaller
than within a twentieth of the time used by individual standard
approaches.Comment: 30 pages, 7 figure
Magnetic dipole excitations in nuclei: elementary modes of nucleonic motion
The nucleus is one of the most multi-faceted many-body systems in the
universe. It exhibits a multitude of responses depending on the way one
'probes' it. With increasing technical advancements of beams at the various
accelerators and of detection systems the nucleus has, over and over again,
surprised us by expressing always new ways of 'organized' structures and layers
of complexity. Nuclear magnetism is one of those fascinating faces of the
atomic nucleus we discuss in the present review. We shall not just limit
ourselves to presenting the by now very large data set that has been obtained
in the last two decades using various probes, electromagnetic and hadronic
alike and that presents ample evidence for a low-lying orbital scissors mode
around 3 MeV, albeit fragmented over an energy interval of the order of 1.5
MeV, and higher-lying spin-flip strength in the energy region 5 - 9 MeV in
deformed nuclei, nor to the presently discovered evidence for low-lying
proton-neutron isovector quadrupole excitations in spherical nuclei. To the
contrary, we put the experimental evidence in the perspectives of understanding
the atomic nucleus and its various structures of well-organized modes of motion
and thus enlarge our discussion to more general fermion and bosonic many-body
systems.Comment: 59 pages, 59 figures, accepted for publication in Rev. Mod. Phys
- …